Question

Help me differentiate y^4-xy^2
So far I have
4y^3dy/dx for y^4....
I get stuck on what rule to use on -xy^2
Chain rule?

Answer 1

product rule.

Answer 2

\[\large
(y^4-xy^2)' = 4y^3y' - \{x * 2yy' + y^2 * 1\} = 4y^3y' - 2xyy'- y^2 \\
\]

Answer 3

\[
\frac{d}{dx}xy^2 = x * \frac{d}{dx}y^2 + y^2 * \frac{d}{dx}x = x * 2yy' + y^2 * 1
\]

Answer 4

thank you !